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Simplifying x2 + 3x + -6552 = 0 Reorder the terms: -6552 + 3x + x2 = 0 Solving -6552 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6552' to each side of the equation. -6552 + 3x + 6552 + x2 = 0 + 6552 Reorder the terms: -6552 + 6552 + 3x + x2 = 0 + 6552 Combine like terms: -6552 + 6552 = 0 0 + 3x + x2 = 0 + 6552 3x + x2 = 0 + 6552 Combine like terms: 0 + 6552 = 6552 3x + x2 = 6552 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 6552 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 6552 + 2.25 Combine like terms: 6552 + 2.25 = 6554.25 2.25 + 3x + x2 = 6554.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 6554.25 Calculate the square root of the right side: 80.958322611 Break this problem into two subproblems by setting (x + 1.5) equal to 80.958322611 and -80.958322611.Subproblem 1
x + 1.5 = 80.958322611 Simplifying x + 1.5 = 80.958322611 Reorder the terms: 1.5 + x = 80.958322611 Solving 1.5 + x = 80.958322611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 80.958322611 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 80.958322611 + -1.5 x = 80.958322611 + -1.5 Combine like terms: 80.958322611 + -1.5 = 79.458322611 x = 79.458322611 Simplifying x = 79.458322611Subproblem 2
x + 1.5 = -80.958322611 Simplifying x + 1.5 = -80.958322611 Reorder the terms: 1.5 + x = -80.958322611 Solving 1.5 + x = -80.958322611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -80.958322611 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -80.958322611 + -1.5 x = -80.958322611 + -1.5 Combine like terms: -80.958322611 + -1.5 = -82.458322611 x = -82.458322611 Simplifying x = -82.458322611Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.458322611, -82.458322611}
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